THEMATIC PROGRAMS

Set Theory and Analysis Program

Coxeter Lecture Series

1) The Continuum Hypothesis and the $\Omega$ Conjecture
2) Strong Axioms: Determinacy and Large Cardinals
3) Extender Sequences and Beyond

One compelling approach to resolving the Continuum Hypothesis is to
look for "generically absolute" theories for $H(\omega_2)$
which informally can be thought of as the structure of all subsets of
the least uncountable cardinal, $\omega_1$, or alternatively as the
structure of all $\omega_1$ sequences of reals numbers.

If the $\Omega$ Conjecture is true the criterion of generic absoluteness
is equivalent to validity in $\Omega$ logic. In this case there {\em
are} such good theories for $H(\omega_2)$ but any such theory necessarily
implies that the Continuum Hypothesis is false.

This analysis draws on the considerable machinery which has been developed
over the last several decades for analyzing inner models in which the
Axiom of Determinacy holds. An important component has been the adapting
of techniques from the study of inner models of large cardinals to the
study of inner models of determinacy.